Simplex inequalities of order and chain polytopes of recursively defined posets
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908631231889408 |
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| author | Freij-Hollanti, Ragnar Lundström, Teemu |
| author_facet | Freij-Hollanti, Ragnar Lundström, Teemu |
| contents | In this paper, we study the simplex faces of the order polytope $\mathcal{O}(P)$ and the chain polytope $\mathcal{C}(P)$ of a finite poset $P$. We show that, if $P$ can be recursively constructed from $\mathbf{X}$-free posets using disjoint unions and ordinal sums, then $\mathcal{C}(P)$ has at least as many $k$-dimensional simplex faces as $\mathcal{O}(P)$ does, for each dimension $k$. This generalizes a previous result of Mori, both in terms of the dimensions of the simplices and in terms of the class of posets considered. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_03557 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simplex inequalities of order and chain polytopes of recursively defined posets Freij-Hollanti, Ragnar Lundström, Teemu Combinatorics In this paper, we study the simplex faces of the order polytope $\mathcal{O}(P)$ and the chain polytope $\mathcal{C}(P)$ of a finite poset $P$. We show that, if $P$ can be recursively constructed from $\mathbf{X}$-free posets using disjoint unions and ordinal sums, then $\mathcal{C}(P)$ has at least as many $k$-dimensional simplex faces as $\mathcal{O}(P)$ does, for each dimension $k$. This generalizes a previous result of Mori, both in terms of the dimensions of the simplices and in terms of the class of posets considered. |
| title | Simplex inequalities of order and chain polytopes of recursively defined posets |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.03557 |